Question

what is the length of the hypotenuse? if necessary, round to the nearest tenth. c = kilometers

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with legs \(a = 56\) km and \(b = 42\) km, the Pythagorean theorem is \(c^{2}=a^{2}+b^{2}\), where \(c\) is the hypotenuse. So \(c^{2}=56^{2}+42^{2}\).

Step2: Calculate \(a^{2}\) and \(b^{2}\)

\(56^{2}=56\times56 = 3136\) and \(42^{2}=42\times42=1764\). Then \(c^{2}=3136 + 1764\).

Step3: Find the sum

\(3136+1764 = 4900\), so \(c^{2}=4900\).

Step4: Solve for \(c\)

Take the square - root of both sides: \(c=\sqrt{4900}=70\) km.

Answer:

70